The Foxes are still stuck in the relegation zone and went down to a 2-1 loss away at Bournemouth on Saturday to further pile the pressure on Brendan Rodgers.
Leicester decided to let Kasper Schmeichel move to Nice in the summer but did not bring in a proper replacement for the Dane.
Danny Ward has looked shaky between the sticks for the Foxes and Rodgers wants to bring in a new goalkeeper in January.
And according to Polish outlet Meczyki, the Premier League outfit are on the verge of getting a deal done to sign Spezia goalkeeper Dragowski.
Spezia signed him from Fiorentina in the summer but he has done enough in the first few months to attract interest from Leicester.
The Foxes are closing in on a deal and it has been claimed that an agreement is in place to sign him.
Rodgers wants to shore up his defence in January and is said to be keen to get an upgrade on Ward.
And the Pole is seen as a better solution than the one Leicester currently have in their squad.
